The ratio in which the plane y - 1 = 0 divides the straight line

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsMultiple Choice Questions

141.

The equation of the plane through the line of intersection of the planes x - y + z + 3 = 0 and x + y + 22 + 1 = 0 and parallel to x-axis is

  • 2y - z = 2

  • 2y + z = 2

  • 4y + z = 4

  • y - 2z = 3


142.

If 3p + 2q = i + j + k and 3p - 2q = i - j - k, then the angle between p and q is

  • π6

  • π4

  • π3

  • π2

     


143.

The point of intersection of the straight line x - 22 = y - 1- 3 = z + 21 with the plane x + 3y - z + 1 = 0 is

  • (3, - 1, 1)

  • (- 5, 1, - 1)

  • (2, 0, 3)

  • (4, - 2, - 1)


144.

If the lines 2x - 12 = 3 - y1 = z - 13 and x + 32 = z + 1p = y + 25 are perpendicular to each other, then p is equal to

  • 1

  • - 1

  • 10

  • 75


Advertisement
145.

The point P(x, y, z) lies in the first octant and its distance from the origin is 12 units. If the position vector of P make 45° and 60° with the x-axis and y-axis respectively, then the coordinates of P are

  • 33, 6, 32

  • 43, 8, 42

  • 62, 6, 6

  • 6, 6, 62


146.

The distance between the planes r . (i + 2j - 2k) + 5 = 0 and r . (2i + 4j - 4k) - 16 = 0 is

  • 3

  • 113

  • 13

  • 133


147.

If the angle θ between the line x + 11 = y - 12 = z - 22 and the plane 2x - y + pz + 4 = 0 is such that sinθ = 13, then the value of p is

  • 0

  • 13

  • 23

  • 53


Advertisement

148.

The ratio in which the plane y - 1 = 0 divides the straight line joining (1, - 1, 3) and (- 2, 5, 4) is

  • 1 : 2

  • 3 : 1

  • 5 : 2

  • 1 : 3


A.

1 : 2

Let the required ratio is λ : 1

By section formula,

P = - 2λ + 1λ + 1, 5λ - 1λ + 1, 4λ + 3λ + 1

which lies on the line y = 1 i . e., 5λ - 1λ + 1 = 1  5λ - 1 = λ + 1  4λ = 2               λ = 12 or λ : 1 = 1 : 2

which is the required ratio.


Advertisement
Advertisement
149.

Equation of the line passing through i + j - 3k and perpendicular to the plane 2x - 4y + 3z + 5 = 0 is

  • x - 12 = 1 - y- 4 = z - 33

  • x - 12 = 1 - y4 = z + 33

  • x - 21 = y + 41 = z - 33

  • x - 1- 2 = 1 - y- 4 = z - 33


150.

The angle between the straight lines x - 1 = 2y + 33 = z +52 and x = 3r + 2; y = - 2r - 1; z = 2, where r is a parameter, is

  • π4

  • cos-1- 3182

  • sin-1- 3182

  • π2


Advertisement